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SSAT Upper Level Math : Acute / Obtuse Triangles

Study concepts, example questions & explanations for SSAT Upper Level Math

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #171 : Properties Of Triangles

The height of a triangle is $\displaystyle 14$, and the base is $\displaystyle 4$. What is the area of the triangle?

Possible Answers:

$\displaystyle 48$

$\displaystyle 28$

$\displaystyle 56$

$\displaystyle 32$

Correct answer:

$\displaystyle 28$

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, substitute in $\displaystyle 4$ for the base and $\displaystyle 14$ for the height.

$\text{Area}=\frac{4\times14}{2}=\frac{56}{2}=28$ $\displaystyle \text{Area}=\frac{4\times14}{2}=\frac{56}{2}=28$

The area of the triangle is $\displaystyle 28$.

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Example Question #172 : Properties Of Triangles

The height of a triangle is 10g $\displaystyle 10g$, and the base is $\displaystyle 6g$. In terms of $\displaystyle g$, what is the area of the triangle?

Possible Answers:

22g $\displaystyle 22g$

40g^2 $\displaystyle 40g^2$

30g^2 $\displaystyle 30g^2$

60g^2 $\displaystyle 60g^2$

Correct answer:

30g^2 $\displaystyle 30g^2$

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, substitute in $\displaystyle 6g$ for the base and 10g $\displaystyle 10g$ for the height.

$\text{Area}=\frac{6g\times10g}{2}=\frac{60g^2}{2}=30g^2$ $\displaystyle \text{Area}=\frac{6g\times10g}{2}=\frac{60g^2}{2}=30g^2$

The area of the triangle is 30g^2 $\displaystyle 30g^2$.

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Example Question #173 : Properties Of Triangles

The base of a triangle is $\displaystyle y$ inches, and the height of the triangle is $\displaystyle 8$ inches. In terms of $\displaystyle y$, what is the area of the triangle?

Possible Answers:

$\displaystyle 8y$ in^2 $\displaystyle in^2$

$\displaystyle 4y$ in^2 $\displaystyle in^2$

$\displaystyle 2y$ in^2 $\displaystyle in^2$

$\frac{y}{2}$ $\displaystyle \frac{y}{2}$ in^2 $\displaystyle in^2$

Correct answer:

$\displaystyle 4y$ in^2 $\displaystyle in^2$

Explanation:

Find the area of the triangle by using the formula $\frac{base\times height}{2}$ $\displaystyle \frac{base\times height}{2}$.

Now, substitute in $\displaystyle y$ for the base and $\displaystyle 8$ for the height.

$\text{Area}=\frac{y\times8}{2}=\frac{8y}{2}=4y$ $\displaystyle \text{Area}=\frac{y\times8}{2}=\frac{8y}{2}=4y$

Don't forget to include the units, $\displaystyle 4y$ in^2 $\displaystyle in^2$

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Example Question #174 : Properties Of Triangles

The base of a triangle is 12x $\displaystyle 12x$, and the height of the triangle is $\displaystyle 5$. If the area of the triangle is 120 $\displaystyle 120$, what is the value of $\displaystyle x$?

Possible Answers:

$\displaystyle 6$

$\displaystyle 60$

$\displaystyle 4$

$\displaystyle 30$

Correct answer:

$\displaystyle 4$

Explanation:

Use the following formula to find the area of a triangle:

$\text{Area}=\frac{base\times height}{2}$ $\displaystyle \text{Area}=\frac{base\times height}{2}$

Now, substitute in 12x $\displaystyle 12x$ for the base, $\displaystyle 5$ for the height, and 120 $\displaystyle 120$ for the area..

Use algebraic opertions to solve for x.

$120=\frac{12x\times5}{2}$ $\displaystyle 120=\frac{12x\times5}{2}$

60x=120 $\displaystyle 60x=120$

x=4 $\displaystyle x=4$

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Example Question #175 : Properties Of Triangles

The height of the triangle is $\displaystyle 5d$, and the base of the triangle is $\displaystyle 8$. If the area of the triangle is $\displaystyle 80$, what is the value of $\displaystyle d$?

Possible Answers:

$\displaystyle 6$

$\displaystyle 8$

$\displaystyle 10$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

Use the formula for the area of a triangle.

$\text{Area}=\frac{base \times height}{2}$ $\displaystyle \text{Area}=\frac{base \times height}{2}$

Substitute in $\displaystyle 8$ for height, $\displaystyle 5d$ for the base, and $\displaystyle 80$ for the area.

From here, use algebraic operations to isolate d on one side and all other numbers on the other side.

$80=\frac{5d\times 8}{2}$ $\displaystyle 80=\frac{5d\times 8}{2}$

40d=160 $\displaystyle 40d=160$

d=4 $\displaystyle d=4$

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SSAT Upper Level Math : Acute / Obtuse Triangles

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #171 : Properties Of Triangles

Example Question #172 : Properties Of Triangles

Example Question #173 : Properties Of Triangles

Example Question #174 : Properties Of Triangles

Example Question #175 : Properties Of Triangles

All SSAT Upper Level Math Resources

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